1. Field of the Invention
The present invention relates to a method for estimation of fundamental matrix in implementing a stereo vision from two cameras. More particularly, the present invention relates to a method for estimation of fundamental matrix, wherein the inlier set is selected in order that the selected correspondence points are evenly distributed in the whole image. According to the method, the whole image is divided into several sub-regions, and the number of the inliers in each sub-region and the area of each region are examined.
2. Description of the Related Art
Stereo vision, a useful technique for obtaining 3-D information from 2-D images, has many practical applications including robot navigation and realistic scene visualization. Given a point in the one image, we find the corresponding point in the other image so that the two points are the projections of the same physical point in space. In this process, the fundamental matrix representing succinctly the epipolar geometry of stereo vision is estimated. The fundamental matrix contains all available information on the camera geometry and it can be computed from a set of correspondence points. Then, the matching process for finding correspondence point in the other image is conducted.
Hereinafter, the epipolar geometry is explained in detail.
Epipolar geometry is a fundamental constraint used whenever two images of a static scene are to be registered. In the epipolar geometry, the relation between two images respectively obtained from different cameras may be explained with a correspondence of a point to a line, rather than a correspondence of a point to a point. Given a point in the one image, we find the corresponding point in the other image so that the two points are the projections of the same physical point in space. These two points are called as “correspondence point”. The plane made by a point X, and two cameras is called as “epipolar plane”. The intersection line made by the epipolar plane and the image plane is called as “epipolar line”. The intersection point made by the image plane and the line linking two cameras is called as “epipole”. Given a point in one image, corresponding point in the second image is constrained to lie on the epipolar line. FIG. 1 is a diagram for explaining the epipolar geometry. All the epipolar geometry is contained in the fundamental matrix.
The epipolar constraint can be written as following Equation 1:x′T Fx=0  [Equation 1]
where, x and x′ are the homogeneous coordinates of two correspondence points in the two images, and
F is the fundamental matrix (3 by 3) that has rank 2, and since it is defined up to a scale factor, there are 7 independent parameters.
From the Equation 1, the fundamental matrix can be estimated linearly, given a minimum of 8 correspondence points between two images. Because the fundamental matrix contains the intrinsic parameters and the rigid transformation between both cameras, it is widely used in various areas such as stereo matching, image rectification, outlier detection, and computation of projective invariants.
Because the fundamental matrix can be estimated from the information of correspondence points, the influence of outlier which exists in the information of correspondence points should be reduced. It is important to select a proper inlier set for a more precise fundamental matrix.
In general, for an optimal solution satisfied in the given data set, wrong data may be sometimes an obstruction in finding the solution, if the data set comprises wrong data. Such wrong data which can be in a given data set are called as “outlier”. Thus, for a precise solution, it is preferable to find a solution after such wrong data are eliminated. It is preferable to distinguish the wrong data from proper data based on a predetermined criterion. Such proper data are called as “inlier”.
According to the prior art, the precision of the fundamental matrix much depends on the selection of inlier set. Therefore, it is important to eliminate the outlier due to the false matching in the information of correspondence points for finding a precise fundamental matrix. The Estimation of fundamental matrix is sensitive to the error, though it can be conducted from the correspondence point set. Therefore, it is important to select inlier set from the correspondence point set.
Several algorithms for the estimation of fundamental matrix are categorized into three methods: the linear method, the iterative method, and the robust method. The linear method and the iterative method use some points to estimate the fundamental matrix.
First, the linear approaches, such as Eight-Point Algorithm, estimate the fundamental matrix by using eight corresponding points. With more than eight points, a least mean square minimization is used, followed by the enforcement of the singularity constraint so that the rank of the resulting matrix can be kept in 2. These approaches have been proven to be fast and easy to implement, but they are very sensitive to image noise.
Second, the iterative methods are based on optimization criteria, such as the distance between points and epipolar lines, or the gradient-weighted epipolar errors. Although these methods are more accurate than the linear method, they are time consuming and much affected by the unavoidable outliers inherent in the given correspondence matches and the error on the point locations.
Finally, the robust methods such as LMedS(Least Median of Square) and RANSAC(Random Sampling Consensus), can cope with either outliers or bad point localization.
RANSAC uses a minimum subset for parameter estimation and the solution is given by the candidate subset that maximizes the number of consistent points and minimizes the residual.
According to the LMedS method, the correspondence point set wherein the median of distance error is least is selected.
However, according to the robust methods, different inlier set is selected whenever this method is conducted since the inlier set for finding the fundamental matrix is selected randomly. Thus, the obtained fundamental matrix is much affected by the selected inlier set. It is probable to estimate the fundamental matrix which has a large error. Further, it is computationally infeasible to consider all possible subsets, since the computation load grows exponentially according to the number of the inliers. Therefore, additional statistical measures are needed to derive the minimum number of sample subsets. In addition, because of the restrictive way of sampling the points randomly, the obtained fundamental matrix can be much changed by which points are selected.